ELECTRICAL POWER GENERATION ECONOMICS.pptx

ecnomics related

1. Module 5
Economics

2. ; A
Economics of Power Generation

Terms considered in power plants:-
+ Connected Load

+ Maximum Demand

« Demand Factor

« Average Load

« Load Factor

* Diversity Factor

+ Plant Capacity Factor

+ Reserve Capacity

« Plant Use Factor

« Plant Utilization Factor

a Loss Factor

ant nfEEE COMMIT Ilüra Karnataka India A

3. Connected Load

e.

It is the sum of continuous rating of all the
equipments connected to the supply system.

Example: If a consumer has connected five
100W bulbs and ten 50W bulbs. Then the
connected load of the consumer

= (5x100W) + (10x50W)
= 1000W
= 1kW

4. Maximum Demand

It is a greatest demand of the load on a power

station during a given period.

+ Maximum demand always less than
connected load.

+ Maximum demand helps to determine the

capacity of the station.

Generating station must be capable of
meeting maximum demand.

5. Demand Factor

¢ It is the ratio of maximum demand on the
power station to the connected load.

« Demand Factor= Maximum Demand
Connected Load

+ Value of demand factor is usually less than
unity because maximum demand on the
power station always less than connected
load.

6. Demand Factor

« If the maximum demand on the power station
is 80MW & the connected load is LOOMW.

Demand factor = 80/100
=0.8

¢ The knowledge of demand factor is vital in
determining the capacity of plant equipments.

7. Average Load

+ The average of loads occurring on the power
station in a given period ( day or month or
year) is called average load or average
demand.

+ Depends on the period average load can be

categorized into Daily average load, Monthly
average load & Yearly average load.

8. Average Load

« Daily average load =
Number of units(kWh) generated in a day
24 hours

+ Monthly average load=
Number of units(kWh) generated in a month

Number of hours in month

9. Load Factor

+ The ratio of average load to the maximum
demand during a given period is known as load
factor.

« Load factor = Average load
Maximum demand
* The load factor may be daily load factor, monthly

load factor or annual load factor if the time
period is considered is a day or month or year.

10. Load Factor

+ Load factor is always less than one because
average load is smaller than maximum
demand.

+ Load factor plays key role in determining the
overall cost per unit generated.

+ Higher load factor, lesser will be the cost per
unit generated.

11. Diversity Factor

The ratio of sum of individual maximum
demands to the maximum demand on the
power station is known as diversity factor.

Diversity factor

= Sum of individual maximum demands

Maximum demand on the power station

Ch Clip sk

12. od
Diversity Factor

* Diversity factor is always greater than one

» Greater diversity factor implies lesser the cost
of power generation.

13. .
Plant Capacity Factor

It is the ratio of actual energy produced to the
maximum possible energy that could have
been produced during a given period.
Plant Capacity Factor

= Actual Energy Produced

Maximum Energy that could have been produced

14. .
Plant Capacity Factor

+ Plant Capacity factor = Average Demand
Plant Capacity

+ Annual Plant Capacity Factor
= Annual kWh output
Plant Capacity x 8760

15. .
Reserve Capacity

« Difference between plant capacity & maximum
demand.

+ Reserve capacity = Plant capacity — Maximum
demand

* The power station is so designed that it has some
reserve capacity for meeting the increased load
demand in future.

+ The installed capacity of the plant is always
somewhat greater than maximum demand on
the plant.

16. Plant Use Factor

It is the ratio of kWh generated to the product
of plant capacity & the number of hours for
which the plant was in operation.
Plant use factor =

Station output in kWh

Plant capacity x Hours of use

17. Plant Use Factor

Eg. A plant having installed capacity of 20MW
produces annual output of 7.35x10%6 kWh
and remains the operation of 2190 hours in a
year. Calculate the plant use factor?

Plant use factor = (7.35x1016)/(20x1013)x(2190)

= 0.167

= 16.7%

18. Loss factor

« Loss factor is an expression of the average
power factor over a given period of time.

« It is used in the energy industry to express the
losses in transmission and distribution from
heat, incomplete combustion of fuels and
other inefficiencies.

+ Power factor only applies to alternating

current (AC). Direct current always has a
power factor of 100%.

19. Plant Utilization Factor

Utilization factor

It is the ratio of present maximum generation of the plant and the installed or the original
design capacity of the plant.

Utilization factor =( Maximum load)/(rated capacity of plant)

7/21/2017 Dept. of EEE, SDMIT, Ujire, Karnataka, India 22

20. Plant Utilization Factor

« In electrical engineering, utilization factor, is
the ratio of the maximum load which could be
drawn to the rated capacity of the system.

* This is closely related to the concept of Load
factor.

« The utilization factor or use factor is the ratio
of the time that a piece of equipment is in use
to the total time that it could be in use.

21. .
Installed Capacity

» It is the designed power generation capacity
of a plant. It is expressed in terms of energy
generated per unit time.

° Megawatts or Megawatt electric (MW or
MWe) is the most commonly used term for
electricity generating plants.

22. .
Units Generated Per Annum

+ kWh generated per annum

* It is often required to find the kWh generated
per annum from maximum demand and load
factor.

* Load factor= Average load/Maximum demand

« Average load= Maximum demand x Load
factor

+ Units generated per annum = Average load (in
kW) x Hours in a year

Dept. of EEE, SDMIT, Ujire, Karnataka, India

23. Units Generated Per Annum
+ Units generated per annum = Average load (in

kW ) x Hours in a year
= Maximum demand x LF x 8760

7/21/2017 Dept. of EEE, SDMIT, Ujire, K

24. .
Numerical Examples

Q1. The maximum demand on the power station

is LOOMW. If the annual load factor is 40%.
Calculate the total energy generated in a year?

HowitosolWe it... PRPPPPPPPLPPP??7?

25. Numerical Examples

Answer1.

Energy generated per year= Maximum demand
x Load factor x Hours in a year.

= (100x 1000)x (0.40) x (8760)
= 350400000 kWh

26. E] Clip sk

Numerical Examples

Q2. A generating station has a connected load of
43MW& a maximum demand of 20 MW. The
units generated being 61.5x10%6 per annum.

Calculate

i)Demand factor

ii) Load factor
PPPPPPPPPPPPPPPPPP

27. Numerical Examples

Answer 2)
i) Demand factor =
= Maximum demand/connected load
= 20/43 = 0.465

Average demand =Units generated per annum/
hours in a year

= 61.5x1016/8760 = 7020kW
Load factor= Average load/Max demand
= 7020/ 20x 103 = 0.351 or 35.1%

28. Load Curve

« The curve showing the variation of load on
the power station with respect to the time is
known as load curve.

* Load on the power station is never constant. It
will vary from time to time.

Peak load

29. Load Curve

¢ The load variations during whole day(24hrs)
recorded hourly and are plotted against time
on the graph. The curve thus obtained is
called daily load curve.

Load in MW
sa
+

5—r ------
ee 1

CC A eo

12 4 8 1216 20 24
un A

(Mid Night) Time of day
Load curve

30. Load Curve

Monthly load curve is obtained from the daily
load curve.

The monthly load curve is generally used to fix
the rate of energy.

The yearly load curve is obtained by
considering monthly load curve of that
particular year.

Yearly load curve used to determine annual
load factor.

31. Load Curve

Importance of load curve

1. The daily load curve shows the variation of load
on the power station during different hours of
the day.

2. The area under daily load curve gives the
number of units generated in the day. ie Units
generated = electrical energy (kWh).

3. The highest point on the daily load curve
represents the maximum demand on the station
on that day.

Average load = (Area under daily load curve)/ 24 hrs

32. Load Curve

Importance of load curve
4. The load curve helps in selecting the size and
number of generating units.

5. The load curve helps in preparing the
operation schedule of the station.

33. Load Duration Curve

« When the load elements of a load curve are
arranged in the order of descending
magnitudes, the curve thus obtained is called
load duration curve.

Load in MW

' ' ' H
Ott ty Ade 4
12 4 8 1216 20 24 0 4 8 12 16 20 24
SER Fr Ben
{Mid Night} Time of day Hours duration
Load curve Load duration curve
(1 (ii)

34. Load Duration Curve

¢ The load duration curve is obtained from the sam
data as the load curve but the ordinates are
arranged in the order of descending magnitudes.

« The maximum load is represented to left &
decreasing loads are represented to right in the
descending order.

¢ The load duration curve gives the data in more
presentable form.

« The area under the load duration curve is equal tc
that of corresponding load curve. The area under
load duration curve (in kWh) will give the unit
generated on that day.

35. PGEC 15EE42 VTU NOTES MODULE 4
Tariff

What you meant by tariff.....?

+ The rate at which the electrical energy is
supplied to a consumer is known as tariff.

The tariff should include the total cost of
producing, supplying electrical energy and the
profit.

Tariff can’t be same for all type of consumers.

e

Tariff depends upon type of consumers.

36. Tariff

+ The supply company (Eg. MESCOM, BESCOM
etc) has to ensure that the tariff is such that it
is not only recover the total cost of producing
electrical energy but also earns the profit on
the capital investment.

e

Suitable rate making for each type of
consumer is complicated process.

37. Tariff

Objectives of tariff

* The electrical energy is sold at such a rate so that it is
not only return the cost but also earns reasonable
profit.

« Recovery of cost of producing electrical energy at the
power station.

« Recovery of cost of the capital investment in the
transmission and distribution system.

* Recovery of cost of operation and maintenance of
supply of electrical energy. (Eg. Metering equipment,
billing equipment etc).

« To obtain profit on the capital investment

38. Tariff

Desirable Characteristics of a Tariff
1. Proper return
. Fairness

Z

3. Simplicity
4. Reasonable profit
5

. Attractive

39. Tariff

Desirable Characteristics of a Tariff

4,

Proper return

Ensure proper return from each consumer
Total receipts from the consumer must be
equal to the cost of producing & supplying
electrical energy plus reasonable profit.

This will enable the electric supply to ensure
continuous and reliable service to the
consumer.

40. C Cig

Tariff

Desirable Characteristics of a Tariff

2. Fairness

¢ It should be fair so that different types of
consumers are satisfied with the rate of charge of
electrical energy.

« Big consumers are charged at the lower rate than
a small consumer.

* Consumers those who having non variable load
should be charged at lower rate as compared to
the consumers who is handling variable load.

41. Tariff

Desirable Characteristics of a Tariff

5. Attractive

+ The tariff should be attractive so that a large
number of consumers are encourage to use
electrical energy.

+ The efforts should be made to fix the tariff in
such a way so that the consumer can pay
easily.

42. Tariff

Types of tariff

. Simple tariff

. Flat rate tariff

. Block rate tariff

. Two part tariff

. Maximum demand tariff
. Power factor tariff

. Three part tariff

not Aa Uy Nba

7/21/2017 Dept. of EEE, SOMIT, Ujire, Karnataka, India

43. Tariff

Types of tariff
1. Simple tariff

+ When there is a fixed rate per unit of energy
consumed. It is called as simple tariff or uniform rate
tariff.

¢ Price charged per unit is constant.

+ It doesn’t vary with the increase or decrease the
number of units consumed.

+ The consumption of electrical energy at the consumer
terminal is recorded by means of energy meter.

+ Simplest tariff & easily understand by the consumer

44. Tariff

Types of tariff
1. Simple tariff
Drawbacks

« No discrimination between different type of
consumer.

+ Cost per unit delivered is high.
« It doesn't encourage the use of electricity

45. Tariff

Types of tariff
2. Flat rate tariff

+ When different types of consumers are charged at
different uniform per unit rate. Then it is called as flat
rate tariff.

+ Consumers are grouped into different classes.

* Each classes of consumers are charged at different
uniform rate.

« Example:- Based on flat rate tariff

The flat rate per kWh for lighting load may be 60 paise
where as it may be 55 paise for power load

« Different classes of consumers are made taking into
account their diversity and load factor.

46. Tariff

Types of tariff

2. Flat rate tariff

Advantages

+ More convenient for different type of consumers
* Calculation is simple

Disadvantages

« Separate meters are required for lighting and power
load. Tariff is expensive & complicated.

+ A particular class of consumer is charged at the same
rate irrespective of the magnitude of energy
consumed.

47. Tariff

Types of tariff

3. Block rate tariff

+ When a given block of energy is charged at a
specified rate and the succeeding block of the
energy are charged at progressively reduced
rate. This type of tariff is called as block rate
tariff.

The energy consumption is divided into blocks
* Price per unit is fixed in each block

e

48. Tariff

Types of tariff

3. Block rate tariff

+ The price per unit in the first block is highest. It is
progressively reduced for the succeeding block of
energy.

Eg. First 30 units charges at the rate of 60 paise
per unit, the next 25 units charges at the rate of
55 paise per unit and remaining additional unit
charges 30 paise per unit.

This type of tariff is applicable for residential &
small consumers.

49. Tariff

Types of tariff

3. Block rate tariff

Advantages

+ Consumer gets an incentive to consume more
electrical energy

¢ This method increases the load factor of the
system & hence the cost of generation is
reduced.

50. PGEC 15EE42 VTU NOTES MODULE 4

Tariff

Types of tariff
3. Block rate tariff
Drawbacks

« Lack of measuring consumers demand

51. C Cig

Tariff

Types of tariff
4. Two Part tariff

« When the rate of electrical energy is charged on tl
basis of maximum demand of the consumer and t
units consumed, it is called as two part tariff.

Total charge made from the consumer is split into
two components ie fixed charges & running charg

« Fixed charges depends upon the maximum demar
of the consumer while the running charges depen
upon the number of units consumed by the
consumer.

52. Tariff

Types of tariff
4. Two Part tariff

* Thus the consumer is charged at a certain amount per
kW of maximum demand plus a certain amount per
kWh of energy consumed.

Total charges=

Rs(b x kW + c x kWh)

b=charge per kW of maximum demand
C=charge per kWh of energy consumed

+ Applicable for industrial consumers who have
appreciable maximum demand.

53. Tariff

Types of tariff

4. Two Part tariff

Advantages

« Itis easily understood by the consumer

* It recovers the fixed charges which depend upon the
maximum demand of consumer but are in depended of the
unit consumed.

Disadvantages

* The consumer has to pay fixed charge irrespective of the
factor whether he has consumed or not consumed electrica
energy.

¢ There is always error in assessing the maximum demand of
the consumer

54. Tariff

Types of tariff

5. Maximum demand tariff

* Itis similar to two part tariff with the only
difference that the Maximum demand is actually
measured by installing maximum demand meter i
the premises of the consumer.

« This removes the objection of two part tariff
where the maximum demand is assessed merely
on the basis of rateable value.

« This tariff is mostly applied to big consumers,
However, it is not suitable for small consumer as 2
separate maximum demand meter is required.

55. Tariff

Types of tariff
6. Power factor tariff

The tariff in which power factor of the consumer”:
load is taken into consideration is known as powe
factor tariff.

In an AC system, power factor plays important rol
A low power factor increases the rating of station
equipment and line losses.

Therefore consumer having low power factor mus
penalised.

56. Tariff

Types of tariff

6. Power factor tariff

Types of power factor tariff

a)kVA maximum demand tariff

+ Itis a modified form of two part tariff

« In this case the fixed charge is made on the basis of maximum
demand in kVA not in kW.

+ As Kva is inversely proportional to power factor, therefore,
consumer having low power factor has to contribute more
towards the fixed charge.

« This tariff has the advantages that it encourages the consume
to operate their appliances and machinery at improved power
factor.

57. Tariff

Types of tariff

6. Power factor tariff

Types of power factor tariff

b)Sliding scale tariff

« This is also know as average power factor tariff

+ In this case, an average power factor, say 0.8 lagging is
taken as the reference .

« If the power factor of the consumer falls below this
power factor , suitable additional charges are made.

+ On the other hand, if the power factor is above the
reference , a discount is allowed to the consumer.

58. PGEC 15EE42 VTU NOTES MODULE 4
Tariff

Types of tariff

6. Power factor tariff

Types of power factor tariff

c)kW 8: kVAR tariff

* In this type both active power (kW) and reactive
power (kVAR) supplied are charged separately.

+ Aconsumer having a low power factor will draw
more reactive power & hence shall have to pay mo
charges.

59. Tariff

Types of tariff

7. Three part tariff

« When the total charge to be made from the
consumer is split into three parts, ie fixed
charge, semi fixed charge and running charge
is known as three part tariff.

« Total charge=

Rs(a + b x KW +c x kWh)

60. Tariff

Types of tariff

7. Three part tariff

« Where ‘a’ is the fixed charge made during each
billing period. It includes interest and
depreciation on the cost of secondary
distribution & labour cost of collecting revenues.

« ‘b’ = charge per kW of maximum demand and ‘c’

= charge per kWh of energy consumed.

Applicable only for big consumers.

61. PGEC 15EE42 VTU NOTES _MODULE 4
T iff

Q1. A consumer has a maximum
demand of 200 kW at 40% load
factor. If the tariff is Rs 100 per kW
maximum demand plus 10 paise p
kWh, find the overall cost per kWh

62. Tariff

Answer:

Unit consumed per year

= Maximum demand x Load factor x Hours in a year
= 200 x 0.40 x 8760 = 700800 kWh

Annual charges = Annual Maximum demand
charges + Annual energy charges

= Rs ( 100 x 200 + 0.1 x 700800) = Rs 90080
Over all cost per kWh = Rs ( 90080/700800)
=Rs 0.1285
= 12.85 paise

63. Power factor

* The cosine angle between voltage and current
in an AC circuit is called power factor.

» The term cos O is called as power factor.

¢ If the circuit is inductive, current lags behind
the voltage and the power factor is referred as
lagging power factor.

¢ If the circuit is capacitive, current leads the
voltage and power factor is said to be leading.

64. Power factor

« The term | cos O is called as
Active component or wattfull
Component

« The term | sin ® is called as
Reactive component or wattless
Component. Fig. 61

+ The reactive component is a measure of power
factor

¢ If the reactive component is small , the phase ang
O is small, hence the power factor cos © is high

65. Power factor

Power triangle Moss
« The analysis of power factor

VI sin y

Can be made in terms of power
Drawn by the AC circuit. me ®

« Each side of the current triangle multiplied by
the voltage ‘V’ then we get the power
triangle.

OA = Vicos and represents the active power in watts or kV
AB VI sin and represents the reactive power in VAR or kV,
OB = VIand represents the apparent power in VA or kVA

66. Power factor

Power triangle
The apparent power in an a.c. circuit has two components viz.
active and reactive power at right angles to each other.
OB” = O4 +AB
(apparent power) = (active power)? + (reactive power)
(EVA? = (KW) + (KVAR)’
OA _ active power _ kW

Power factor, cos d = = 2 A
OB apparent power kVA

Thus the power factor of a circuit may also be defined as the ratio of active power to the
apparent power. This is a perfectly general definition and can be applied to all cases, what-
ever be the waveform.

The lagging* reactive power is responsible for the low power factor. It is clear from the
power triangle that smaller the reactive power component, the higher is the power factor of
the circuit.

kw

kVAR = kVA sin = ar

ANAND — Ars A

sind

67. Power factor

Definitions of power factor

Power factor = cos — cosine of angle between V and I

Power factor = E - Resistance
Z Impedance
O e E VIcos@ _ Active power

VI Apparent Power

68. Power factor

Disadvantages of low power factor

« Large kVA rating of the equipment

kW

KVA = 0

It is clear that kVA rating of the equipment is inversely proportional to power factor. The sm:
the power factor, the larger is the kVA rating. Therefore, at low power factor, the kVA rating oi
equipment has to be made more, making the equipment larger and expensive.

* Greater Conductor size
qe 2" -
V, cos 6
It is clear from above that for fixed power and voltage, the load current is inversely proportion:
to the power factor. Lower the power factor, higher is the load current and vice-versa.

69. Power factor

Disadvantages of low power factor
* Large copper losses

The large current at low power factor causes more PR losses in al
elements of the supply system. This results in poor efficiency.

« Poor voltage regulation

The large current at low lagging power factor causes greater
voltage drops ın alternators, transformers, transmission lines and distributors. This results
in the decreased voltage available at the supply end, thus impairing the performance of
utilisation devices. In order to keep the receiving end voltage within permissible limits,
extra equipment (i.e., voltage regulators) is required.

70. Power factor

« Reduced handling capacity of the system

The lagging power factor reduces the hand
capacity of all the elements of the system. It is because the reactive component of cur
prevents the full utilisation of installed capacity.

71. Power factor

Causes of low power factor

Low power factor is undesirable from economic point of view. Normally, the power factor o;
whole load on the supply system in lower than 0-8. The following are the causes of low power fa:
(i) Most of the a.c. motors are of induction type (10 and 36 induction motors) which have
lagging power factor. These motors work at a power factor which is extremely smal
light load (0-2 to 0-3) and rises to 0-8 or 0-9 at full load.
(ii) Are lamps, electric discharge lamps and industrial heating furnaces operate at low lag
power factor.
(iii) The load on the power system is varying ; being high during moming and evening and lc
other times. During low load period, supply voltage is increased which increases
magnetisation current. This results in the decreased power factor.

72. Power factor

Power factor improvement

The low power factor is mainly due to the fact that
most of the loads are inductive & therefore takes
lagging current.

In order to improve the power factor, some device
taking leading power should be connected in parallel
with the load.

One of such device is called capacitor.

The capacitor draws a leading current & partly or
completely neutralise the lagging reactive component
of the load current.

This raises the power factor of the load.

73. Power factor

Power factor improvement

(ii)

74. Power factor

Power factor improvement
Equipments for power factor improvements
¢ Static capacitor

« Synchronous Condenser

« Phase advancers

75. Power factor

Power factor improvement
1.Static capacitor

The power factor can be improved by connecting
capacitors in parallel with the equipment operating at
lagging power factor.

The capacitor generally called as static capacitor draws |
leading current, which will partially or completely
neutralizes the lagging reactive component of the load
current.

This raises the power factor of the load.

For the three phase load capacitor can be connected
either in delta or star.

Static capacitors are invariantly used for power factor

76. Power factor

LM
Power factor improvement equipments >
1.Static capacitor

3-4 Load
==

1 cc

0) un (ii)

77. Power factor

Power factor improvement equipments

1.Static capacitor

Advantages

« Have low losses

* It require little maintenance as there are no
rotating part

« They can easily installed as they are light and
require no foundation

78. Power factor

Power factor improvement equipments

1.Static capacitor

Disadvantages

« Short service of life (8 to 10 years)

« They are easily damaged if the voltage
exceeds rated value

+ Once the capacitor is damaged, their repair is
uneconomical.

79. Power factor

Power factor improvement equipments
2.Synchronous condenser

« Asynchronous motor takes a leading current
when over excited and, therefore, behaves as a
capacitor.

« Over excited synchronous motor running on no
load is known as synchronous condenser.

» When such a machine is connected parallel with
the supply, it takes a leading current which partly
neutralize the lagging reactive component of the
load. Thus power factor is improved.

80. Power factor

‘Syncteonous Condenser

Power factor improvement equipments
2.Synchronous condenser

1 ih

3-6 Load

3-9 Synchronous:
impor Fig. 6.5

81. Power factor

Power factor improvement equipments
2.Synchronous condenser

Explanation

The 36 load te
current J, at low lagging power factor cos @,. The synchronous condenser takes a current J, wi
leads the voltage by an angle 6,*. The resultant current J is the phasor sum of I, and J, and |
behind the voltage by an angle 6. It is clear that 0 is less than 6, so that cos ( is greater than cos
Thus the power factor is increased from cos 6; to cos ©. Synchronous condensers are generally 1
at major bulk supply substations for power factor improvement.

82. Power factor

Power factor improvement equipments

2.Synchronous condenser

Advantages

« By varying the field excitation, the magnitude of
current drawn by the motor can be changed by
an amount. This helps in achieving stepless
control of power factor.

+ Motor winding have high thermal stability to
short circuit current.

+ The fault can be removed easily.

83. Power factor

Power factor improvement equipments
2.Synchronous condenser
Disadvantages

There are considerable losses in the motor
The maintenance cost is high
It produces noise

Except size in above 500kVA, the cost is greater than
that of static capacitor of the same rating.

As synchronous motor has no self starting torque,
therefore, an auxiliary equipment has to provide for
this purpose.

84. Power factor

Power factor improvement equipments

3. Phase advancers

» Used to improve the power factor of induction motors.

* The low power factor of induction motor is due to the
fact that its stator winding draws exciting current which
lags behind the supply voltage by 90 degree.

+ Ifthe exciting ampere turns can be provided from
some other AC source, then the stator winding will be
relieved of exciting current and the power factor of the
motor can be improved.

¢ This job is accomplished by phase advancers which is
simply an AC exciter.

85. Power factor

Power factor improvement equipments

3. Phase advancers

¢ The phase advancer is mounted on the same
shaft as the main motor & is connected to the
main circuit of motor.

It provides exciting ampere turns to the rotor
circuit at slip frequency, the induction motor
can be made to operate on leading power
factor like an over excited synchronous motor.

86. Power factor

Power factor improvement equipments

3. Phase advancers

Advantages

+ The exciting ampere turns are supplied at slip
frequency, therefore lagging kVAR drawn by the
motor is reduced.

+ Conveniently used where the synchronous motor
is inadmissible.

Disadvantages

« This method is not economical for the motor
below 200 H.P

87. Power factor

Power factor improvement equipments

3. Phase advancers

Advantages

+ The exciting ampere turns are supplied at slip
frequency, therefore lagging kVAR drawn by the
motor is reduced.

+ Conveniently used where the synchronous motor
is inadmissible.

Disadvantages

« This method is not economical for the motor
below 200 H.P

88. Power factor

Importance of Power Factor Improvement

(i) For consumers:

+ Consumer has to pay electricity charges for
his maximum demand in kVA plus the units
consumed.

+ If the consumer improves power factor there
is a reduction in maximum kVA demand and
achieve annual saving.

89. Power factor

Importance of Power Factor Improvement
(ii) For Generating station:
« Astation output in kW = kVA x cos O

+ Therefore the number of units supplied
depends on the power factor.

« The greater the power factor of the generating
station, the higher is the kWh it delivers to the
system.

90. Variable Load on Power System

¢ The load on the power system varies from
time to time due to the uncertain demands of
the consumers and is known as variable load
on the station.

+ The power station is designed to meet the
load requirement of the consumers.

« The load demand of one consumer at any

time may be different from that of the other
consumer.

91. 2

Variable Load on Power System

Effects of variable load on power station:-

+ Need for additional equipment: The variable
load on power station necessititates to have
additional equipment. Eg. Consider steam
power plant, In order to produce variable
power the supply of raw material need to be
adjusted. Therefore additional equipment
need to be installed for accomplish the task.

Clip

92. Ch Clip

Variable Load on Power System

Effects of variable load on power station:-

« Increase in production cost: The variable load
on the plant increases the cost of production
of electrical energy. An alternator operates at
maximum efficiency near its rated capacity.
Instead of single alternator, alternators of
different capacities need to be installed. The
use of number of generating units increases
production cost.

93. ene .
Classification of cost

In general the cost of generating electrical energy can
be divided into the following three elements.

1. Fixed cost
2. Semi-fixed cost

3. Running or Operating cost

94. Classification of cost

1. Fixed cost:

The capital investment of land, salaries of
high officials, annual expenditure of central
organisation & Interest on the capital cost of
land are called as fixed cost.

Fixed cost is independent of maximum
demand & energy output.

95. Classification of cost

2. Semi-fixed cost:

« The semi-fixed cost is due to annual interest €
depreciation on the capital cost of generating
plant, transmission and distribution network,
building 8: other civil work, taxes, Insurance
charges & clerical works.

Semi-fixed cost depends upon the maximum

demand (kW) and independent of energy
output (kWh).

96. Classification of cost

3. Running or Operating cost:

« The cost depends upon the number of hours
the plant is in operation or upon the number
of units of electrical energy generated or
energy output.

¢ Similarly it contains cost of water, cost of
lubricating oil, maintenance & repair cost of
equipments, wages & salaries of maintenance
and operating staffs.

97. Classification of cost

« Total annual cost incurred in the power
generation is represented by the expression

E= a +bxkW +cxkWh

a, b and care constants.

« Fixed and semi-fixed cost being independent of
the amount of energy generated is also called as
“ standing cost”.

98. Cost Analysis of Power Plants

* The generation cost can be broadly be divided into (i)
Fixed cost and (ii) Operating or Running cost.

(i) Fixed cost

-Interest on total investment

-Taxes & Insurances

-Salaries of High officials

-Cost of design, planning & building
-Cost of dam

-Earth work, road & rail

-Civil work

99. Cost Analysis of Power Plants

(ii) Operating or Running cost:
-Depends on extent of operation
-Amount of power generation
-Fuel cost

- Lubricating oil cost

- Water

- Maintenance & Repair

- Salaries of supervisory staff

100. Cost Analysis of Power Plants

« Fixed & Operating (Running) cost of Hydro
Power Plants:

Fixed cost:

-Cost of preliminary survey & Investigation
-Purchase of land

-Design cost & Construction cost

-Cost of transportation facilities & Civil engg. Works
-Salaries of high officials

Operating (Running) cost:

-Cost of Lubricating oil & Maintenance cost

101. .
Cost Analysis of Power Plants

« Fixed & Operating (Running) cost of Steam
Power Plants:
Fixed cost: Cost of land, design cost,
Equipment installation charge, Power house
building, testing, taxes & depreciation etc.
Operating cost: Fuel cost, cost of water,
condenser cost, lubricating oil cost,
maintenance cost & supervisory charge.

102. E Cli

Cost Analysis of Power Plants

» Fixed €: Operating (Running) cost of Nuclear
Power Plants:
Fixed cost: Construction cost, cost of reactors
and auxiliaries, taxes & Insurance.
Running Cost: Cost of cooling water, cost of
operating staff

tip

103. Ch Clip

Interest

Interest is the earning power of money.

It represents the growth of capital per unit
period.

The period may be a month, a quarter, semi
annual or a year.

Interest is the income produced by money
that is lent or loaned.

Simple interest & Compound interest are the
type of interest.

104. Ch Clip

Interest

« Usually money is borrowed from banks or
insurance companies or other financial
institutions for big projects such as generating
plants.

« At the end of year, the under taking is
required to pay the interest on the capital
cost.

« Interest need to be paid back.

105. Interest

+ Simple interest
F= Total sum realized after n years
n= no. of periods
i= Interest, i= PnR

+ Compound interest

Fn= P*(1+i)4n

106. Ch Clip

Depreciation

What is Depreciation.....?

« After a certain time the power plant equipment is
to be replaced because of physical €: functional
reasons.

« Eg. Plant has worn out & become unfit for further
use (physical reason) , capacity of the power
plant become inadequate due to load growth
(functional reason).

¢ In order to calculate depreciation charge, it is

necessary to estimate the useful life of the power
plant.

107. Depreciation

Methods of Depreciation

1;

2
3
4.
5

Straight line depreciation

. Sum of years digits depreciation

. Declining balance depreciation

Diminishing value method

. Sinking fund depreciation

108. Ch Clip

Depreciation

Methods of Depreciation

1.Straight line depreciation

« There is reduction in value of equipment & other
property of the plant every year due to
depreciation.

A constant depreciation charge is made every
year on the basis of total depreciation and the
useful life of the property.

The annual depreciation charge equals to the
total depreciation divided by the useful life of
the property.

109. Depreciation

Methods of Depreciation
1.Straight line depreciation
Annual depreciation charge= P-S

n
P= initial cost of the equipment

n = useful life of the equipment in years

S= scrap value or salvage value after the useful
life of the plant.

110. Depreciation

Methods of Depreciation
1.Straight line depreciation

Example: If the initial cost of the equipment is
Rs 100000 and its scrap value is 10000 after
the useful life of 20 years. Calculate annual
depreciation charges?

Annual depreciation= Total depreciation

Useful life

111. Depreciation

Methods of Depreciation
1.Straight line depreciation
100000 - 10000

20

= Rs. 4500/-

112. Straight Line Depreciati greg

Depreciation

Dollars (5)

Methods of Depreciation :

1.Straight line depreciation met

Drawbacks

¢ Assumption of constant depreciation charge is
not correct.

* It does not account for the interest which may
be drawn during accumulation.

113. er
Depreciation

Methods of Depreciation

2. Sum of years digit depreciation

* In this method depreciation is determined by
finding the sum of digits using the following
formulae
N= n(n+1)/ 2
n= life of equipment
N= Sum of digit

114. Depreciation

Methods of Depreciation

2. Sum of years digit depreciation
First year, D=(n/N) *(P-L)
Second year, D= ((n-1)/N)*(P-L)
Third year, D= ((n-2)/N)* (P-L)

L- Salvage value or scrap valu
P- Initial investment

115. Depreciation

Methods of Depreciation

3. Declining Balance Depreciation

* Depreciation charges are larger in the earlier
stage

« In this method Depreciation rate can be
reestablished

116. Depreciation

Methods of Depreciation
3. Declining Balance Depreciation

D= 1- (L/P)A(1/N)

D- Annual depreciation rate

L- Salvage value or scrap value
P- Initial investment

N- Duration / Useful life

117. Depreciation

Methods of Depreciation

4. Diminishing value Depreciation

« Similar to declining balance method

« Depreciation charge is fixed for every year
« More rational than straight line method

Depreciation value D= 1- (L/P)4(1/N)

Depreciation after n years= P*(1- D)4n

118. Depreciation

Methods of Depreciation
4. Diminishing value Depreciation

Deminishing Balance Method
Straight-Line Method of Depreciation en
2,
1,200
1,000 + (sides, |
Pr É
Eos 2 «== Annual Deprecaiton Charge
i $ 1500
a em» Anmual Deprecaiton Charge 3
= 60 E
3 3
H mn E 1000
= á
a
200 500
1 2 3 4 5 6 7 8 9 10
Ver 1 2 3 4 5 6 7 8 9 10
Year

119. Ch Clip

Depreciation

Methods of Depreciation
5.Sinking Fund Depreciation

« Fixed depreciation charge is made every year &
interest compounded on it annually.

« Interest is considered.

Depreciation charge implies cost of replacement
of equipment after its useful life.

Depreciation charge= total annual installment +
interest accumulations.

120. Depreciation

Methods of Depreciation

5.Sinking Fund Depreciation

« “Total fund must be equal to the cost of
replacement of equipment”.

+ Cost of replacement=P-S (a)

P= Initial investment or Capital

S= Scrap value or Salvage value

121. er
Depreciation

Methods of Depreciation

5.Sinking Fund Depreciation

Total fund= q(1+r)*n — 1/r (b)

According to sinking fund method , total fund
equals to cost of replacement.

Equate (a) and (b)

122. Depreciation

Methods of Depreciation

5.Sinking Fund Depreciation
P-S=q(1+r)An-1/r

Sinking fund q= (P-S)* (r/(1+r)4n - 1))

Where r/(1+r)An -1 is called sinking fund factor.
P-Initial value of equipment

n - Useful life of equipment in years

S- Scrap value after useful life
r — Annual rate of interest expressed as a decimal

123. Depreciation

Methods of Depreciation

5.Sinking Fund Depreciation
Advantages

« Interest is considered

« Economically sound

» Provide cash for replacement

« Enable drawing up of balance sheet

124. Depreciation

Methods of Depreciation
5.Sinking Fund Depreciation
Disadvantages

« Calculation is difficult

« Accounting is rather difficult

125. Numerical Problems

Q1. Calculate the depreciation rate using the
i)straight line & ii) sum of year’s digit for the
data given below: Salvage value Lis Rs O, Life
of equipment , n=5 years, Initial expenditure ,
P=Rs 1,50,000, for a declining balance method
use a 200% rate.

126. Numerical Problems

i) Straight line method
D= (P-L)/n

=(1,50,000 — 0)/5

= 30,000 per year

127. Numerical Problems

ii)Sum of year’s digit method
N= n(n+1)/2

5(5+1)/2

N= 15
Di=(n/N)*P =50,000/-
D2= ((n-1)/N)*P = 40,000/-
D3= ((n-2)/N)*P = 30,000/-
D4= ((n-3)/N)*P = 20,000/-
D5=((n-4)/N)*P = 10,000/-

128. Numerical Problems

Q2. A transformer costing Rs 90,000 has an
useful life of 20 years .Determine the annual
depreciation charge using straight line
method. Assume the salvage value of the
equipment to be Rs 10,000/-.

P= 90,000/-
S= 10,000/-
N= 20 years

129. Numerical Problems

Q2. Solution

Annual depreciation charge =(P-S) /n
= (90,000 - 10,000)/20
= Rs.4000/-

130. Numerical Problems

Q3. A distribution transformer costs Rs 2,00,000
and has a useful life of 20 years. If the salvage
value is Rs 10,000 & the rate of annual
compound interest is 8%, calculate the
amount to be saved annually for replacement
of the transformer after the end of 20 years
by sinking fund method.

131. Numerical Problems

Q3. Solution
P= 2,00,000/-
n= 20 years
S= 10,000/-
r=8%

132. Numerical Problems

Q3. Solution
q =(P—S) ( r/ (1+r)4n -1)

Rs 4153/-